Students As Creators - Not Curators - Of Math | ECOO BIT14 Conference Slide Deck
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Transcript of Students As Creators - Not Curators - Of Math | ECOO BIT14 Conference Slide Deck
Students As Creators - Not Curators - Of Math
@MathletePearce
www.tapintoteenminds.com
Kyle Pearce
tapintoteenminds.com/bit14
ABOUT MEWindsor, ONMath Teacher / Math CoachApple Distinguished EducatorApple Authorized TrainerGoogle Certified Teacher
@MathletePearcewww.tapintoteenminds.com
WHERE
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@MathletePearcewww.tapintoteenminds.com
Student Learning Need
@MathletePearcewww.tapintoteenminds.com
Inability to demonstrate understanding of algebra through multiple representations.
Theory of Action
Understanding of Algebraic Representations
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Theory of Action
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Contextual Problems
Theory of Action
@MathletePearcewww.tapintoteenminds.com
Theory of Action
Contextual Problems
Promote Creation of Concrete Representations Through Discovery
@MathletePearcewww.tapintoteenminds.com
Contextual Problems
Theory of Action
Understanding of Algebraic Representations
Promote Creation of Concrete Representations Through Discovery
4 -Part Math Lesson
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3
Inquiry
Consolidation
Inquiry 1.
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Minds On
Consolidation
-Part Math Lesson4
Minds On Inquiry1.
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2.
Consolidation
-Part Math Lesson4
Minds On
Consolidate
Inquiry1.
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2.
3. Connections
-Part Math Lesson4
Connections
Minds On
Consolidate
Inquiry1.
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2.
3. 4.
-Part Math Lesson4
Workflow
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Workflow
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Workflow
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Workflow
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GoodNotes 4
Connections
Minds On
Consolidate
Inquiry1.
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2.
3. 4.
-Part Math Lesson4
Previous Day
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Previous Day
@MathletePearcewww.tapintoteenminds.com
Mr. Pearce stacks reams of paper with a thickness of 4.95 cm vertically against a
wall. If the height of the room is 273 cm, how many reams of paper would he
need to reach the ceiling?
Previous Day
@MathletePearcewww.tapintoteenminds.com
Mr. Pearce stacks reams of paper with a thickness of 4.95 cm vertically against a
wall. If the height of the room is 273 cm, how many reams of paper would he
need to reach the ceiling?FUN, RIGHT?
Previous Day
@MathletePearcewww.tapintoteenminds.com
Mr. Pearce stacks reams of paper with a thickness of 4.95 cm vertically against a
wall. If the height of the room is 273 cm, how many reams of paper would he
need to reach the ceiling?
Mr. Pearce stacks reams of paper with a thickness of 4.95 cm vertically against a
wall. If the height of the room is 273 cm, how many reams of paper would he
need to reach the ceiling?
Previous Day
@MathletePearcewww.tapintoteenminds.com
Mr. Pearce stacks reams of paper with a thickness of 4.95 cm vertically against a
wall. If the height of the room is 273 cm, how many reams of paper would he
need to reach the ceiling?
Previous Day
@MathletePearcewww.tapintoteenminds.com
Mr. Pearce stacks reams of paper with a thickness of 4.95 cm vertically against a
wall. If the height of the room is 273 cm, how many reams of paper would he
need to reach the ceiling?
Previous Day
@MathletePearcewww.tapintoteenminds.com
Mr. Pearce stacks reams of paper with a thickness of 4.95 cm vertically against a
wall. If the height of the room is 273 cm, how many reams of paper would he
need to reach the ceiling?
Previous Day
@MathletePearcewww.tapintoteenminds.com
How many packs of paper would it take to reach the ceiling?
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
How many packs of paper would it take to reach the ceiling?
4. Consolidate3. Connections
2. Inquiry
Previous Day
273
cm
4.95
cm
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper would it
take to reach the ceiling?
4. Consolidate3. Connections
2. Inquiry
Previous Day
273 cm
4.95 cm
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper would it
take to reach the ceiling?
4. Consolidate3. Connections
2. Inquiry
Previous Day
273 cm
4.95 cm= 55.15
How many packs of paper will it take to reach
a height of 273 cm?
How many packs of paper would it take to reach the ceiling?
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
How many packs of paper will it take to reach a
height of 273 cm? 4. Consolidate3. Connections
2. Inquirypacks of paper
height
How many packs of paper would it take to reach the ceiling?
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
How many packs of paper will it take to reach a
height of 273 cm? 4. Consolidate3. Connections
2. Inquirypacks of paper
height
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
0 0
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
0 01 4.95
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
0 01 4.952 9.9
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
0 01 4.952 9.9… …
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
0 01 4.952 9.9… …
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry
packs of paperheight :
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry
packs of paper
height
4.95
cm
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry
packs of paper
height4.95 cm
1 pack
273
cm
How many
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
x ?
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
x 55.15
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
x 55.15
x ?
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
x 55.15
x 55.15
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?55.15
x 55.15
x 55.15packs
Consolidate
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
1. Minds On
1. Minds On
Consolidate
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-Part Math Lesson
Consolidate
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
How many ‘thick’ packs of paper would it take to reach the ceiling?
1. Minds On
Consolidate
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
How many ‘thick’ packs of paper would it take to reach the ceiling?
1. Minds On6
cm
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
How many ‘thick’ packs of paper would it take to reach
the ceiling?
1. Minds On6
cm
4. Consolidate3. Connections
2. Inquiry
4. Consolidate3. Connections
2. Inquiry1. Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson4
How many ‘thick’ packs of paper would it take to reach the ceiling?
2. Inquiry
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
4. Consolidate
2. Inquiry
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
How tall is the table?
4. Consolidate
Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow tall is the table?
2. Inquiry
Minds On
Inquiry2. -Part Math Lesson
4. Consolidate3. Connections
2. Inquiry1. Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson4
Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
3. Connections
Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow tall is the table?
3. Connections13
0.7
5 cm
Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow tall is the table?13
0.7
5 cm
packs of paper heightIndependent Dependent
Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow tall is the table?13
0.7
5 cm
packs of paper heightIndependent Dependent
5packs13
0.7
55
Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow tall is the table?13
0.7
5 cm
packs of paper heightIndependent Dependent
5packs
5
130
.75
Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow tall is the table?13
0.7
5 cm
packs of paper heightIndependent Dependent
5packs
130.755
Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow tall is the table?13
0.7
5 cm
packs of paper heightIndependent Dependent
5packs
130.755 )x y(
Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math LessonHow tall is the table?13
0.7
5 cm
packs of paper heightIndependent Dependent
5packs
130.755( )x ySlope
3. Connections
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4. Consolidate3. Connections
2. Inquiry1. Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson4
4. Consolidate
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2. Inquiry
4. Consolidate
@MathletePearcewww.tapintoteenminds.com
2. Inquiry
4. Consolidate3. Connections
2. Inquiry1. Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson4
GoodNotes 4
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The Next Day…
GoodNotes 4
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The Next Day…
GoodNotes 4
@MathletePearcewww.tapintoteenminds.com
The Next Day…
GoodNotes 4
How tall is this table?
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The Next Day…
GoodNotes 4
How tall is this table?
142
.75
cm
@MathletePearcewww.tapintoteenminds.com
The Next Day…
GoodNotes 4
How tall is this table?
142
.75
cm
100
.75
cm
@MathletePearcewww.tapintoteenminds.com
The Next Day…
GoodNotes 4
How tall is this table?
142
.75
cm
100
.75
cm
6 c
m
142
.75
cm
100
.75
cm
Equations Given 2 Points
142
.75
cm
100
.75
cm
Equations Given 2 Points
142
.75
cm
100
.75
cm
Equations Given 2 Points
142
.75
cm
100
.75
cm
Equations Given 2 Points
142
.75
cm
100
.75
cm
Equations Given 2 Points
Volume of a Sphere
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Volume of a Sphere
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4 r3πr3π33
=V
Volume of a Sphere
@MathletePearcewww.tapintoteenminds.com
4 r3πr3π33
=V
or4 r3πr3π
33=V
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@MathletePearcewww.tapintoteenminds.com
Discovering the Formula for Volume of a Sphere
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@MathletePearce tapintoteenminds.com
Recall Volume of a Cylinder
r2π
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Recall Volume of a Cylinder
r2π
V = Area of Base
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Recall Volume of a Cylinder
r2π
V = πr2
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Recall Volume of a Cylinder
r2π
V = x Heightπr2
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Recall Volume of a Cylinder
r2π
hV = πr2 h
Recall Volume of a Cylinder
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r2π
hV = πr2h
3
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r2π
hV = πr2h
3
Recall Volume of a
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r2π
hV = πr2h
3
Recall Volume of a
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r2π
hV = πr2h
3
Recall Volume of a Cone
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r2π
hV = πr2h
3
Recall Volume of a Cone
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r2π
Recall Volume of a Cone
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r2π
Recall Volume of a Cone
+
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r2π
Recall Volume of a Cone
+ =
@MathletePearce tapintoteenminds.com
r2π
h
Recall Volume of a Cone
+ =
@MathletePearce tapintoteenminds.com
r2π
Recall Volume of a Cone
+ =h
@MathletePearce tapintoteenminds.com
r2π
Recall Volume of a Cone
+ =h
@MathletePearce tapintoteenminds.com
r2π
Recall Volume of a Cone
+ = h
@MathletePearce tapintoteenminds.com
r2π
Recall Volume of a Cone
+ =
@MathletePearce tapintoteenminds.com
r2π
Recall Volume of a Cone
+ =r
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r2π
Recall Volume of a Cone
+ =r
@MathletePearce tapintoteenminds.com
r2π
Recall Volume of a Cone
+ = r
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r2ππr2h
3
Recall Volume of a Cone
+ =
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r2ππr2h
3
Recall Volume of a Cone
+ =πr2h
3+
@MathletePearce tapintoteenminds.com
r2ππr2h
3
Recall Volume of a Cone
+ =πr2h
3+ = Volume of
a Sphere
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r2ππr2h
3
Recall Volume of a Cone
+ = hr
πr2h3
+ = Volume ofa Sphere
r
@MathletePearce tapintoteenminds.com
r2ππr2h
3
Recall Volume of a Cone
+ = hr
πr2h3
+ = Volume ofa Sphere
r
@MathletePearce tapintoteenminds.com
r2ππr2h
3
Recall Volume of a Cone
+ = hr
πr2h3
+ = Volume ofa Sphere
r
@MathletePearce tapintoteenminds.com
r2ππr2h
3
+ = hr
πr2h3
+ = Volume ofa Sphere
r
r
r
@MathletePearce tapintoteenminds.com
r2ππr2h
3
+ = hr
πr2h3
+ = Volume ofa Sphere
r
r
r
@MathletePearce tapintoteenminds.com
r2ππr h
3
+ =πr h
3+ = Volume of
a Sphere
r
r
r
rh
r
r
r
r
@MathletePearce tapintoteenminds.com
r2ππr h
3
+ =πr h
3+ = Volume of
a Sphere
r
r
r
rh
r r r r( )+ ( )+
@MathletePearce tapintoteenminds.com
r2ππr
3
+ =πr
3+ = Volume of
a Sphere
r
r
r
rh
r r r r( )+ ( )+
@MathletePearce tapintoteenminds.com
r2ππr
3
+ =πr
3+ = Volume of
a Sphere
r
r
r
rh
rr rr( )+ ( )+
@MathletePearce tapintoteenminds.com
r2ππr
3
+ =πr
3+ = Volume of
a Sphere
r
r
r
rh
( )2r ( )2rr r
rπrπ
@MathletePearce tapintoteenminds.com
r2ππr3
+ =πr3
+ = Volume ofa Sphere
r
r
r
rh
2 2r r
rπrπ
@MathletePearce tapintoteenminds.com
r2π3
+ =
3+ = Volume of
a Sphere
r
r
r
rh
2 2r r
r3πr3π
@MathletePearce tapintoteenminds.com
r2π3
+ =
3+ = Volume of
a Sphere
r
r
r
rh
2 2
r3πr3π
@MathletePearce tapintoteenminds.com
r2π3
+ =
3+ = Volume of
a Sphere
r
r
r
rh
2 2
r3πr3π
@MathletePearce tapintoteenminds.com
r2π3
+ =
3+ = Volume of
a Sphere
r
r
r
rh
2 2
r3πr3π
@MathletePearce tapintoteenminds.com
r2π3
+ =
3+ = Volume of
a Sphere
r
r
r
rh
2 2( )
r3πr3π
@MathletePearce tapintoteenminds.com
r2π3
+ =
3+ = Volume of
a Sphere
r
r
r
rh
2 2( )
r3πr3π
@MathletePearce tapintoteenminds.com
r2π3
+ =
3+ = Volume of
a Sphere
r
r
r
rh
22( )
4 r3πr3π
@MathletePearce tapintoteenminds.com
r2π3
+ =
3= Volume of
a Sphere
r
r
r
rh
( )
4 r3πr3π
@MathletePearce tapintoteenminds.com
r2π3
+ =
3= Volume of
a Sphere
r
r
r
rh
4 r3πr3π
@MathletePearce tapintoteenminds.com
r2π33=V
Volume ofa Sphere
4 r3πr3π
@MathletePearce tapintoteenminds.com
r2π33=V or 4 r3πr3π
33
Volume ofa Sphere
=V
@MathletePearcewww.tapintoteenminds.com
Contextual Problems
Theory of Action
Understanding of Algebraic Representations
Promote Creation of Concrete Representations Through Discovery
or…
@MathletePearcewww.tapintoteenminds.com
Assist Students In Creating Their OWN Math Understanding,
@MathletePearcewww.tapintoteenminds.com
Assist Students In Creating Their OWN Math Understanding,
or…
@MathletePearcewww.tapintoteenminds.com
Assist Students In Creating Their OWN Math Understanding,
Force Student Curation and Consumption of OUR Math Understanding
or…
Resources & FeedbackPlease complete the survey
to help me improve
Your feedback is appreciated!
tapintoteenminds.com/bit14
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Reach Out!
www.tapintoteenminds.com
Kyle Pearce
@MathletePearce
tapintoteenminds.com/bit14